Chapter 2. Material & methods
2.4. Analysis
2.4.2. Comparative analysis of neuronal network oscillations
With the differences between beta oscillations seen in the different modalities, this project required the development of analysis software capable of disentangling information about the underlying neuronal networks generating the oscillations. The analysis also required ability to compare the similarities in responses to the manipulations presented to beta oscillations in the sensorimotor cortex recorded from different conditions. The analysis approaches presented here were therefore developed with these key points, and concerns from above, in mind.
The recorded signals from MEG and in vitro experiments were analysed with custom- made MatLab scripts. The initial step was to process 30s Morelet-Wavelet spectrograms, 1-100 Hz. Morelet-wavelet spectrograms display the change in frequency and power over time. The time is found on the x-axis and the frequency on the y-axis. The power is displayed as colour changes, usually on the RGB colour spectrum, e.g. red colours indicate high power and blue less power. Morelet-wavelet spectrograms and associated PSDs were calculated for each sample (for a recording period of 30s the number of samples in an epoch will be related to the sampling rate; in vitro: 1000kHz, e.g. 30000 samples; MEG: 600 Hz, e.g. 36000 samples) in each time-period for each subject or recording, using a sliding window approach. For specific details of the outputs from the custom-made MatLab scripts, see section 2.4.2.6.
2.4.2.1. Oscillatory frequency analysis
Measurements of oscillatory frequency usually assume that the frequency is constant throughout the measurement period. As a consequence, the frequency measurement is dependent upon the frequency variability and power at each frequency over the measurement window. To circumvent this, frequency is here determined from a sliding window PSD measurement from each sample in the time period and, independent of power, the mean frequency is derived from this. An example of the differences in peak frequency result between approaches can be seen in figure 2.9 below.
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Figure 2. 9. The averaged PSD plot of the spontaneous oscillatory activity from MI and SI. The peak values for the beta range in this plot are 24.5 Hz for MI and 22 Hz for SI. The mean peak frequency using the sliding window approach were 22.2 Hz for MI, illustrated by the blue vertical line, and 18 Hz for SI, illustrated by the light green vertical line.
2.4.2.2. Oscillatory power
Similar to the observation of frequency, power at the peak is dependent upon the variability of the frequency over time and the power at each peak frequency. Here, oscillatory power is analysed by taking a measurement of power at the peak frequency at each sample throughout the time period of interest. This provides a measurement of power at the frequency peak, these individual measurements of power at the peak frequencies are averaged to provide the mean peak power for the whole epoch. The current analysis approach will provide a more accurate representation of the oscillatory power during the epoch. In the example provided in the figure 2.9, above, the beta peak power in MI was 3.9 nAm and 2.6 nAm in SI. Using the different analysis approach we developed for this project, the mean peak power was 4.44±1.53 nAm in MI, and 3.06±1.09 nAm in SI.
2.4.2.3. Frequency distribution
As discussed above, the measurement of power in a pre-defined frequency band is dependent upon changes in frequency and also the morphology of the frequency peak. As a result, these approaches are insensitive to frequency variability, condition-dependent shifts and changes in frequency distribution. The distribution of the oscillatory peak, which is indicative of frequency composition and distribution networks involved in the measured neuronal oscillation, is addressed by using the objective measure of full-width half-
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FWHM output provides an objective measure of variability and network distribution through its peak sharpness and frequency width. The FWHM width is combined with the mean frequency peak to provide a shape measurement of the oscillatory peak for each individual recording. The peak shape indicates the presence of underlying oscillatory signals, see figure 2.11 below. If one network is responsible for an oscillation, e.g. driven by a single oscillator it should have an even distribution around the mean frequency. If this is not the case it suggests that additional oscillators are contributing to the activity.
Figure 2. 11. Ai-Cii. Schematic pictures showing the oscillatory PSDs and FWHM. In Ai and Aii (left top and bottom), the individual PSD profiles can be seen, these are averaged as seen in Bi and Bii (middle top and bottom). The existence and characteristics of more than one network oscillator and its frequency can be determined by looking at the shape of the peak in conjunction with the mean frequency of the peak. The average PSD on the bottom row (Bii) is broader and most likely contains frequency contributions from more than one oscillation frequency. The FWHM plots, seen in Ci and Cii (right top and bottom), show the individual frequency ranges and the mean frequency peak, which in Cii indeed shows contribution from more than one oscillation.
Figure 2. 10. Schematics showing full-width at half-maximum amplitude (FWHM). Difficulties in determining the frequency width of an oscillatory peak in a PSD, due to baseline fluctuations, are circumvented by using the FWHM measure. Right peak has wider FWHM.
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For each recording one FWHM value is produced, see figure 2.12a-b for examples of this. These can then be averaged over the group to provide the mean FWHM, giving a representation of the frequency range of the network responsible for the ongoing oscillations in the area/condition of interest, see figure 2.12c below for an example of this.
Figure 2. 12a-c. FWHM measurements in individual recordings from motor cortex superficial and deeper layers (MI LIII and LV) is seen in a and b, respectively in left and right top. FWHM values are averaged across the recording groups to provide the mean FWHM for the group in the area/condition of interest, shown in c (bottom).
2.4.2.4. Frequency variability and stationarity
As discussed previously, the mean frequency, amplitude and distribution are subject to the variability of the oscillation over time. In order to further disentangle the composition of the oscillatory signals the peak frequency distribution was quantified. This provides an understanding of how the peak frequency varies over the measurement epoch. We used a histogram approach, whereby the peak frequency is computed for each sample in the measurement epoch and assigned to the appropriate frequency bin (1Hz bin widths were used). The frequency distribution is thus presented as a power-independent representation frequency and indicates the contribution of frequency variability or Stationarity to the oscillatory profile and mean peak frequency. See figure 2.13a for an
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example of the power-independent frequency distribution histogram. Additionally, the power in each frequency bin can be computed to provide a normalised power/sample distribution for each frequency. This provides a method of determining the proportional contribution of each frequency to the PSD, see figure 2.13b below for an example of the frequency distribution when power per sample is taken into account. This is useful to indicate changes in power for a specific peak frequency.
Figure 2. 13a-b. The peak frequency distribution in MI can be plotted independent of amplitude to provide information about the non-stationarity in peak frequency, seen in a (left). The power per sampled peak frequency can also be taken into account to establish if there are any changes in power for a specific peak frequency, seen in b (right). The black arrows indicate where most of the peak frequency measurements from all samples were found, e.g. the frequency distribution peaks.
2.4.2.5. Oscillatory power and state change
Oscillatory measurements, whether made from E/MEG or in vitro recordings, show a large degree of non-uniformity in the power of the signal. For example, measurements of the beta band in motor cortex shows periodic bursts of power, particularly in Parkinson’s disease patients. However, although these phenomena have the capacity to impact strongly upon the observed changes in power, there is rarely any consideration made for the power composition or intrinsic variability. When determining the impact of a change in conditions it is important to understand the nature of that change. Here, to disentangle this, an objective measurement of the power in the signal was used by sorting the power data from each sample in terms of amplitude. This distribution was then ranked in order of amplitude, converted to a zero-mean signal and cumulative summation applied. The effect of this is an objective sorting of power into low and high power states defined as above or below a minimum change point, e.g. the point of difference between the states. Samples were then determined as high or low power and the contribution of this determined before and after intervention. This addresses the question of the contribution of so called ‘oscillatory bursting’, see figure 2.14 below for an example. The mean power in the upstate, e.g. the state above the change point, and the downstate, e.g. below the change
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point, can be calculated to provide a quantitative determination of the variability of power. These can then be averaged over the group and compared between conditions and areas. Changes in power states after an intervention indicate a change in the pattern of activity.
Figure 2. 14. Oscillatory power state analysis of MI oscillations in one participant. The oscillatory power peaks in the beta band (15-35 Hz) are plotted over time per recording. The top box illustrates the peak power values, while the bottom box illustrates which samples were above the change point.
2.4.2.6. MatLab scripts
Custom-made MatLab scripts were designed to extract these oscillatory frequency and power characteristics. These scripts used the data from the sliding window Morelet- Wavelet spectrograms/PSDs and provided the following specific outputs: mean peak frequency ± standard deviation, mean power at the frequency peak ± standard deviation, mean full width half-maximum ± standard deviation, mean % of samples at peak frequency ± standard deviation, mean % samples at peak frequency ±5Hz ± standard deviation, mean % samples at peak frequency ±10Hz ± standard deviation, % up-and downstate, mean power in up- and downstate. There custom-made MatLab scripts which tested the results with t-tests and the statistical outputs were t-statistics and p-values. We tested between ‘before’ and ‘after’ time periods in the same participants and slices, and between oscillatory signals within the same participants or slices. Furthermore, the integration of in vitro signals for a designated location into an in silico aggregation was done by averaging the Morelet-wavelet spectrograms into one dataset. These integrated datasets were then analysed in the same way as the in vitro and MEG data.
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